Later, Goldberg closed his studio to work at Disney Animation Studios, Burbank, California, to work on the film Aladdin, for which he became the lead animator on the character Genie, and later the lead animator on Phil in Hercules (1997). Goldberg also was the co-director of Disney's 1995 feature Pocahontas. During his time as the lead animator for the Genie, he also provided the majority of the original animation for MC Skat Kat's "Big Time" music video, which was finished in 1992 but left unaired.

Goldberg not only served as the director of animation for Warner Bros.' 2003 live-action/animation hybrid feature Looney Tunes: Back in Action, but he also provided the voices of Marvin the Martian, Tweety, and Speedy Gonzales. Although Back in Action wasn't commercially successful at the box office, it was met with relatively positive reviews from film critics, and Goldberg was nominated for an Annie Award for Outstanding Directing in an Animated Feature Production for his animation direction. He animated the title sequence of Metro-Goldwyn-Mayer's 2006 remake of The Pink Panther, with Bob Kurtz of Kurtz and Friends.